Question

If a,b,c are in A.P, then show that a(b+c)/bc,b(c+a)/ca and c(a+b)/ab are also in A.p

Answer 1

Answer:

step by step:

abc are in AP

a(b+c)/bc , b(c+a)/ca , c(a+b)/ab

on adding 1 to it , we get

a(b+c)/bc + 1 , b(c+a)/ca + 1 , c(a+b)/ab + 1 = (ab + bc + ac)/bc , (ab + bc + ac)/ac , (ab + bc + ac)/ab

On dividing by (ab + bc + ac) , we get

= 1/bc , 1/ac , 1/ab

On multiplying by abc , we get

= a ,b ,c

So, a(b+c)/bc , b(c+a)/ca , c(a+b)/ab are in A.P

hope this helps